Image-domain Material Decomposition Research Articles

Image-domain material decomposition for dual-energy CT using unsupervised learning with data-fidelity loss.

Dual-energy computed tomography (DECT) and material decomposition play vital roles in quantitative medical imaging. However, the decomposition process may suffer from significant noise amplification, leading to severely degraded image signal-to-noise ratios (SNRs). While existing iterative algorithms perform noise suppression using different image priors, these heuristic image priors cannot accurately represent the features of the target image manifold. Although deep learning-based decomposition methods have been reported, these methods are in the supervised-learning framework requiring paired data for training, which is not readily available in clinical settings. This work aims to develop an unsupervised-learning framework with data-measurement consistency for image-domain material decomposition in DECT. The proposed framework combines iterative decomposition and deep learning-based image prior in a generative adversarial network (GAN) architecture. In the generator module, a data-fidelity loss is introduced to enforce the measurement consistency in material decomposition. In the discriminator module, the discriminator is trained to differentiate the low-noise material-specific images from the high-noise images. In this scheme, paired images of DECT and ground-truth material-specific images are not required for the model training. Once trained, the generator can perform image-domain material decomposition with noise suppression in a single step. In the simulation studies of head and lung digital phantoms, the proposed method reduced the standard deviation (SD) in decomposed images by 97% and 91% from the values in direct inversion results. It also generated decomposed images with structural similarity index measures (SSIMs) greater than 0.95 against the ground truth. In the clinical head and lung patient studies, the proposed method suppressed the SD by 95% and 93% compared to the decomposed images of matrix inversion. Since the invention of DECT, noise amplification during material decomposition has been one of the biggest challenges, impeding its quantitative use in clinical practice. The proposed method performs accurate material decomposition with efficient noise suppression. Furthermore, the proposed method is within an unsupervised-learning framework, which does not require paired data for model training and resolves the issue of lack of ground-truth data in clinical scenarios.

Artificial intelligence-based image-domain material decomposition in single-energy computed tomography for head and neck cancer.

While dual-energy computed tomography (DECT) images provide clinically useful information than single-energy CT (SECT), SECT remains the most widely used CT system globally, and only a few institutions can use DECT. This study aimed to establish an artificial intelligence (AI)-based image-domain material decomposition technique using multiple keV-output learning of virtual monochromatic images (VMIs) to create DECT-equivalent images from SECT images. This study involved 82 patients with head and neck cancer. Of these, the AI model was built with data from the 67 patients with only DECT scans, while 15 patients with both SECT and DECT scans were used for SECT testing. Our AI model generated VMI50keV and VMI100keV from VMI70keV equivalent to 120-kVp SECT images. We introduced a loss function for material density images (MDIs) in addition to the loss for VMIs. For comparison, we trained the same model with the loss for VMIs only. DECT-equivalent images were generated from SECT images and compared with the true DECT images. The prediction time was 5.4s per patient. The proposed method with the MDI loss function quantitatively provided more accurate DECT-equivalent images than the model trained with the loss for VMIs only. Using real 120-kVp SECT images, the trained model produced precise DECT images of excellent quality. In this study, we developed an AI-based material decomposition approach for head and neck cancer patients by introducing the loss function for MDIs via multiple keV-output learning. Our results suggest the feasibility of AI-based image-domain material decomposition in a conventional SECT system without a DECT scanner.

IMD-MTFC: Image-Domain Material Decomposition via Material-Image Tensor Factorization and Clustering for Spectral CT

Spectral computed tomography (CT) provides multispectral X-ray information that can be used for quantitative material-specific imaging compared to the conventional CT. However, the low-count photon rate in a single energy bin may lead to highly noisy measurements with compromised material contrast and accuracy. Moreover, the complicated material decomposition process is an ill-posed inverse problem, which is sensitive to noise. In this work, we develop an image-domain material decomposition method via material-image tensor factorization and clustering (IMD-MTFC) for spectral CT to obtain high-precision material-specific images. Specifically, a set of image patches is extracted from the normalized material-specific image tensors decomposed by the direct inversion (DI). Then, each of them is clustered in a given nonlocal neighboring area to explore the nonlocal self-similarity of material-specific images. Furthermore, the low-rank regularized Kronecker-basis-representation tensor factorization is employed to incorporate the sparsity and redundant correlation across the material-specific images. The split-Bregman is employed to optimize the model by dividing it into several subproblems. The performance of our method is validated with numerically simulated mouse projections, physical phantom, and preclinical experiments. The results confirm that the IMD-MTFC method outperforms other state-of-the-art competing methods.

Mineral quantitative characterization method based on basis material decomposition model by dual-energy computed tomography.

Dual-energy computed tomography (DECT) can reconstruct electron density ρe and effective atomic number Zeff distribution for material discrimination. Image-domain basis material decomposition (IBMD) method is a widely used DECT method. However, IBMD method cannot be used for mineral identification directly due to limitations of complex basis material determination, beam hardening artifacts, and inherent errors caused by approximate empirical formulas. This study proposes an improved IBMD (IIBMD) method to overcome the above limitations. In IIBMD method, the composition of basis material is optimized to obtain accurate decomposition coefficients, which enables accurate ρe and Zeff distribution. Moreover, the thickness of basis material is optimized to reduce the effect of beam hardening. Furthermore, two formulas in place of empirical formulas are proposed to calculate ρe and Zeff. Finally, a threshold technique is applied to separate different mineral phases. Numerical simulations and practical experiments using a photon-counting detector CT system are implemented to verify IIBMD method. Results show that the relative errors of ρe and Zeff for seven common minerals are down to 5%, lower than most of the existing DECT methods for rocks. Reasonable volume fraction results of mineral phases are thus obtained through threshold segmentation. This study demonstrates that the proposed IIBMD method has high practical value in mineralogical identification.

Spectral CT Image-Domain Material Decomposition via Sparsity Residual Prior and Dictionary Learning

The spectral computed tomography (CT) system based on a photon-counting detector (PCD) can quantitatively analyze the material composition of the inspected object by material decomposition. Nonetheless, the raw projection of spectral CT is frequently disturbed by noise and artifacts, resulting in poor quality material decomposition images. Recently, a generalized dictionary learning based image-domain material decomposition (GDLIMD) to obtain high-quality material images. DL has great advantages in noise suppression and artifacts, while its protection of the fine structure and edge information is insufficient. To address this limitation, we proposed a sparsity residual prior and dictionary learning (SRPDL) algorithm for spectral CT image-domain material decomposition. The SRPDL method retains the noise-resistance performance of dictionary learning (DL) while introducing the pixel-value-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{0} $ </tex-math></inline-formula> norm constraint to guide the material decomposition process by using the structural redundancy information between the prior image and the material images, which further improves structure protection and reduces material misclassification. We conducted numerical simulations, physical phantom, and preclinical experiments to validate and evaluate the SRPDL method. The results demonstrate that the proposed SRPDL method obtained better material decomposition accuracy than the state-of-the-art methods in noise reduction and edge protection.

An improved iterative neural network for high-quality image-domain material decomposition in dual-energy CT.

Dual-energy computed tomography (DECT) has widely been used in many applications that need material decomposition. Image-domain methods directly decompose material images from high- and low-energy attenuation images, and thus, are susceptible to noise and artifacts on attenuation images. The purpose of this study is to develop an improved iterative neural network (INN) for high-quality image-domain material decomposition in DECT, and to study itsproperties. We propose a new INN architecture for DECT material decomposition. The proposed INN architecture uses distinct cross-material convolutional neural network (CNN) in image refining modules, and uses image decomposition physics in image reconstruction modules. The distinct cross-material CNN refiners incorporate distinct encoding-decoding filters and cross-material model that captures correlations between different materials. We study the distinct cross-material CNN refiner with patch-based reformulation and tight-frame condition. Numerical experiments with extended cardiac-torso phantom and clinical data show that the proposed INN significantly improves the image quality over several image-domain material decomposition methods, including a conventional model-based image decomposition (MBID) method using an edge-preserving regularizer, a recent MBID method using prelearned material-wise sparsifying transforms, and a noniterative deep CNN method. Our study with patch-based reformulations reveals that learned filters of distinct cross-material CNN refiners can approximately satisfy the tight-framecondition. The proposed INN architecture achieves high-quality material decompositions using iteration-wise refiners that exploit cross-material properties between different material images with distinct encoding-decoding filters. Our tight-frame study implies that cross-material CNN refiners in the proposed INN architecture are useful for noise suppression and signalrestoration.

A generalized simultaneous algebraic reconstruction technique (GSART) for dual-energy X-ray computed tomography.

Dual-energy computed tomography (DECT) is a widely used and actively researched imaging modality that can estimate the physical properties of an object more accurately than single-energy CT (SECT). Recently, iterative reconstruction methods called one-step methods have received attention among various approaches since they can resolve the intermingled limitations of the conventional methods. However, the one-step methods typically have expensive computational costs, and their material decomposition performance is largely affected by the accuracy in the spectral coefficients estimation. In this study, we aim to develop an efficient one-step algorithm that can effectively decompose into the basis material maps and is less sensitive to the accuracy of the spectral coefficients. By use of a new loss function that employs the non-linear forward model and the weighted squared errors, we propose a one-step reconstruction algorithm named generalized simultaneous algebraic reconstruction technique (GSART). The proposed algorithm was compared with the image-domain material decomposition and other existing one-step reconstruction algorithm. In both simulation and experimental studies, we demonstrated that the proposed algorithm effectively reduced the beam-hardening artifacts thereby increasing the accuracy in the material decomposition. The proposed one-step reconstruction for material decomposition in dual-energy CT outperformed the image-domain approach and the existing one-step algorithm. We believe that the proposed method is a practically very useful addition to the material-selective image reconstruction field.

Direct Iterative Basis Image Reconstruction Based on MAP-EM Algorithm for Spectral CT

Spectral CT can separate basis materials, and thus it can provide information on material characterization and quantification. Such information can benefit various clinical applications. However, the presence of non-ideal effects in X-ray imaging systems limits the accuracy of basis images. To achieve high accuracy of material decomposition and high quality of basis images, a novel direct iterative basis material image reconstruction based on maximum a posteriori expectation–maximization algorithm (MAP-EM-DD) is proposed. Furthermore, by incorporating polar coordinate transformation into MAP-EM-DD, MAP-EM-PT-DD is proposed. The iterative formulas of MAP-EM-DD and MAP-EM-PT-DD are derived. To evaluate the proposed methods, a simulated cylinder phantom with inserts that contain polyethylene, hydroxyapatite, salt water, air, and aluminum is established. The methods are quantitatively evaluated for comparative studies. Results show that the proposed methods can remarkably reduce the noise of basis images and error of material decomposition and improve the contrast-to-noise ratios (CNRs) of each material-specific region. Compared with the image domain material decomposition based on FBP algorithm (FBP-IDD), MAP-EM-DD can reduce the noise levels of basis images ranging from 57.4 to 63.6% and the error levels of each material-specific region from 31.7 to 62.1%. Simultaneously, the CNRs of each material-specific region are improved ranging from 63.8 to 237.3%. Compared with MAP-EM-DD, MAP-EM-PT-DD can reduce the noise levels of basis images ranging from 21.4 to 23.6%, the error levels of each material-specific region ranging from 1.9 to 36.3%, and the reconstruction time of basis images by 14.1%.

Dictionary learning based image-domain material decomposition for spectral CT

The potential huge advantage of spectral computed tomography (CT) is that it can provide accurate material identification and quantitative tissue information by material decomposition. However, material decomposition is a typical inverse problem, where the noise can be magnified. To address this issue, we develop a dictionary learning based image-domain material decomposition (DLIMD) method for spectral CT to achieve accurate material components with better image quality. Specifically, a set of image patches are extracted from the mode-1 unfolding of normalized material images decomposed by direct inversion to train a unified dictionary using the K-SVD technique. Then, the DLIMD model is established to explore the redundant similarities of the material images, where the split-Bregman is employed to optimize the model. Finally, more constraints (i.e. volume conservation and the bounds of each pixel within material maps) are integrated into the DLIMD model. Numerical phantom, physical phantom and preclinical experiments are performed to evaluate the performance of the proposed DLIMD in material decomposition accuracy, material image edge preservation and feature recovery.

Image-domain Material Decomposition for Spectral CT using a Generalized Dictionary Learning.

The spectral computed tomography (CT) has huge advantages by providing accurate material information. Unfortunately, due to the instability or overdetermination of material decomposition model, the accuracy of material decomposition can be compromised in practice. Very recently, the dictionary learning based image-domain material decomposition (DLIMD) can obtain high accuracy for material decompositions from reconstructed spectral CT images. This method can explore the correlation of material components to some extent by training a unified dictionary from all material images. In addition, the dictionary learning based prior as a penalty is applied on material components independently, and many parameters would be carefully elaborated in practice. Because the concentration of contrast agent in clinical applications is low, it can result in data inconsistency for dictionary based representation during the iteration process. To avoid the aforementioned limitations and further improve the accuracy of materials, we first construct a generalized dictionary learning based image-domain material decomposition (GDLIMD) model. Then, the material tensor image is unfolded along the mode-1 to enhance the correlation of different materials. Finally, to avoid the data inconsistency of low iodine contrast, a normalization strategy is employed. Both physical phantom and tissue-synthetic phantom experiments demonstrate the proposed GDLIMD method outperforms the DLIMD and direct inversion (DI) methods.

DECT-MULTRA: Dual-Energy CT Image Decomposition With Learned Mixed Material Models and Efficient Clustering.

Dual-energy computed tomography (DECT) imaging plays an important role in advanced imaging applications due to its material decomposition capability. Image-domain decomposition operates directly on CT images using linear matrix inversion, but the decomposed material images can be severely degraded by noise and artifacts. This paper proposes a new method dubbed DECT-MULTRA for image-domain DECT material decomposition that combines conventional penalized weighted-least squares (PWLS) estimation with regularization based on a mixed union of learned transforms (MULTRA) model. Our proposed approach pre-learns a union of common-material sparsifying transforms from patches extracted from all the basis materials, and a union of cross-material sparsifying transforms from multi-material patches. The common-material transforms capture the common properties among different material images, while the cross-material transforms capture the cross-dependencies. The proposed PWLS formulation is optimized efficiently by alternating between an image update step and a sparse coding and clustering step, with both of these steps having closed-form solutions. The effectiveness of our method is validated with both XCAT phantom and clinical head data. The results demonstrate that our proposed method provides superior material image quality and decomposition accuracy compared to other competing methods.

Photon-counting cine-cardiac CT in the mouse.

The maturation of photon-counting detector (PCD) technology promises to enhance routine CT imaging applications with high-fidelity spectral information. In this paper, we demonstrate the power of this synergy and our complementary reconstruction techniques, performing 4D, cardiac PCD-CT data acquisition and reconstruction in a mouse model of atherosclerosis, including calcified plaque. Specifically, in vivo cardiac micro-CT scans were performed in four ApoE knockout mice, following their development of calcified plaques. The scans were performed with a prototype PCD (DECTRIS, Ltd.) with 4 energy thresholds. Projections were sampled every 10 ms with a 10 ms exposure, allowing the reconstruction of 10 cardiac phases at each of 4 energies (40 total 3D volumes per mouse scan). Reconstruction was performed iteratively using the split Bregman method with constraints on spectral rank and spatio-temporal gradient sparsity. The reconstructed images represent the first in vivo, 4D PCD-CT data in a mouse model of atherosclerosis. Robust regularization during iterative reconstruction yields high-fidelity results: an 8-fold reduction in noise standard deviation for the highest energy threshold (relative to unregularized algebraic reconstruction), while absolute spectral bias measurements remain below 13 Hounsfield units across all energy thresholds and scans. Qualitatively, image domain material decomposition results show clear separation of iodinated contrast and soft tissue from calcified plaque in the in vivo data. Quantitatively, spatial, spectral, and temporal fidelity are verified through a water phantom scan and a realistic MOBY phantom simulation experiment: spatial resolution is robustly preserved by iterative reconstruction (10% MTF: 2.8–3.0 lp/mm), left-ventricle, cardiac functional metrics can be measured from iodine map segmentations with ~1% error, and small calcifications (615 μm) can be detected during slow moving phases of the cardiac cycle. Given these preliminary results, we believe that PCD technology will enhance dynamic CT imaging applications with high-fidelity spectral and material information.

Image domain dual material decomposition for dual-energy CT using butterfly network.

Dual-energy CT (DECT) has been increasingly used in imaging applications because of its capability for material differentiation. However, material decomposition suffers from magnified noise from two CT images of independent scans, leading to severe degradation of image quality. Existing algorithms exhibit suboptimal decomposition performance because they fail to fully depict the mapping relationship between DECT images and basis materials under noisy conditions. Convolutional neural network exhibits great promise in the modeling of data coupling and has recently become an important technique in medical imaging application. Inspired by its impressive potential, we developed a new Butterfly network to perform the image domain dual material decomposition. The Butterfly network is derived from the model of image domain DECT decomposition by exploring the geometric relationship between the mapping functions of the data model and network components. The network is designed as the double-entry double-out crossover architecture based on the decomposition formulation. It enters a pair of dual-energy images as inputs and defines the ground true decomposed images as each label. The crossover architecture, which plays an important role in material decomposition, is designed to implement the information exchange between the two material generation pathways in the network. The proposed network is further applied on the digital phantom and clinical data to evaluate its performance. The qualitative and quantitative evaluations of the material decomposition of digital phantoms and clinical data indicate that the proposed network outperforms its counterparts. For the digital phantom, the proposed network reduces the standard deviation (SD) of noise in tissue, bone, and mixture regions by an average of 95.75% and 86.58% compared with the direct matrix inversion and the conventional iterative method, respectively. The line profiles and image biases of the decomposition results of digital phantom indicate that the proposed network provides the decomposition results closest to the ground truth. The proposed network reduces the SD of the noise in decomposed images of clinical head data by over 90% and 80% compared with the direct matrix inversion and conventional iterative method, respectively. As the modulation transfer function decreases to 50%, the proposed network increases the spatial resolution by average factors of 1.34 and 1.17 compared with the direct matrix inversion and conventional iterative methods, respectively. The proposed network is further applied to the clinical abdomen data. Among the three methods, the proposed method received the highest score from six radiologists in the visual inspection of noise suppression in the clinical data. We develop a model-based Butterfly network to perform image domain material decomposition for DECT. The decomposition results of digital phantom validate its capability ofdecomposing two basis materials from DECT images. The proposed approach also leads to higherdecomposition quality in noise suppression on clinical datasets as compared with those using conventional schemes.

Improved Material Decomposition With a Two-Step Regularization for Spectral CT

One of the advantages of spectral computed tomography (CT) is it can achieve accurate material components using the material decomposition methods. The image-based material decomposition is a common method to obtain specific material components, and it can be divided into two steps: image reconstruction and post material decomposition. To obtain accurate material maps, the image reconstruction method mainly focuses on improving image quality by incorporating regularization priors. Very recently, the regularization priors are introduced into the post material decomposition procedure in the iterative image-based methods. Since the regularization priors can be incorporated into image reconstruction and post image-domain material decomposition, the performance of regularization by combining these two cases is still an open problem. To realize this goal, the material accuracy from those steps are first analyzed and compared. Then, to further improve the accuracy of decomposition materials, a two-step regularization based method is developed by incorporating priors into image reconstruction and post material decomposition. Both numerical simulation and preclinical mouse experiments are performed to demonstrate the advantages of the two-step regularization based method in improving material accuracy.

Adaptive Nonlocal Means Method for Denoising Basis Material Images From Dual-Energy Computed Tomography.

We propose an adaptive nonlocal means approach for image-domain material decomposition in low-dose dual-energy micro-computed tomography. The key idea is to create a distribution map for decomposition error and assign a smooth weight for a given pixel. This method is applied to the decomposed images of 3 basis materials: bone, soft tissue, and gold in our applications. We assume that bone and gold cannot coexist in the same pixel and regroup these basis materials into 2 categories. For soft tissue, the proposed algorithm is implemented in a noniterative mode. For bone and gold, an iterative mode is used and followed by a postiteration process. Both our numerical simulation and in vivo preclinical experiment results show that the proposed adaptive nonlocal means outperforms other state-of-the-art denoising algorithms, such as the original nonlocal means and total variation minimization methods.

Material decomposition with prior knowledge aware iterative denoising (MD-PKAID)

Dual- or multi-energy CT, also known as spectral CT, obtains x-ray attenuation measurements at two or more energy spectra, allowing quantification of materials with different compositions. This process is known as material decomposition, which is the basis for a number of spectral CT applications. The conventional image-domain basis material decomposition is based on a least-squares fitting between the underlying material-specific images and the measured source spectral CT images (i.e. energy-bin or energy-threshold CT images), and a non-iterative solution based on matrix inversion can be derived for this process. However, due to its ill-conditioned nature, the material decomposition process is intrinsically susceptible to noise amplification. Hence, material-specific images can be contaminated by the presence of strong noise, which compromises the conspicuity of small objects, and hinders the delineation of anatomical regions of interest and associated pathology. In this work, we describe an image domain material decomposition framework with prior knowledge aware iterative denoising (MD-PKAID). The proposed framework exploits the structural redundancy between the individual material-specific images and the source spectral CT images to retain structural details in denoised material-specific images. It directly treats material decomposition as a regularized optimization problem with spectral CT images measured with different energy spectra as inputs. Phantom, in vivo animal and human data were acquired on a research whole-body photon-counting-detector-based CT system and a dual-source, dual-energy CT system to test the proposed method. The phantom results show that the proposed MD-PKAID can reduce the root-mean-square-error of basis material quantification by 75% compared to the standard material decomposition based on matrix inversion, while preserving structural details and image resolution in the material-specific images. The initial in vivo results demonstrate that the proposed method can improve delineation of small vasculature features in iodine-specific images while reducing image noise.

MARS-MD: rejection based image domain material decomposition

This paper outlines image domain material decomposition algorithms that have been routinely used in MARS spectral CT systems. These algorithms (known collectively as MARS-MD) are based on a pragmatic heuristic for solving the under-determined problem where there are more materials than energy bins. This heuristic contains three parts: (1) splitting the problem into a number of possible sub-problems, each containing fewer materials; (2) solving each sub-problem; and (3) applying rejection criteria to eliminate all but one sub-problem's solution. An advantage of this process is that different constraints can be applied to each sub-problem if necessary. In addition, the result of this process is that solutions will be sparse in the material domain, which reduces crossover of signal between material images. Two algorithms based on this process are presented: the Segmentation variant, which uses segmented material classes to define each sub-problem; and the Angular Rejection variant, which defines the rejection criteria using the angle between reconstructed attenuation vectors.

Using edge-preserving algorithm with non-local mean for significantly improved image-domain material decomposition in dual-energy CT

Increased noise is a general concern for dual-energy material decomposition. Here, we develop an image-domain material decomposition algorithm for dual-energy CT (DECT) by incorporating an edge-preserving filter into the Local HighlY constrained backPRojection reconstruction (HYPR-LR) framework. With effective use of the non-local mean, the proposed algorithm, which is referred to as HYPR-NLM, reduces the noise in dual-energy decomposition while preserving the accuracy of quantitative measurement and spatial resolution of the material-specific dual-energy images. We demonstrate the noise reduction and resolution preservation of the algorithm with an iodine concentrate numerical phantom by comparing the HYPR-NLM algorithm to the direct matrix inversion, HYPR-LR and iterative image-domain material decomposition (Iter-DECT). We also show the superior performance of the HYPR-NLM over the existing methods by using two sets of cardiac perfusing imaging data. The DECT material decomposition comparison study shows that all four algorithms yield acceptable quantitative measurements of iodine concentrate. Direct matrix inversion yields the highest noise level, followed by HYPR-LR and Iter-DECT. HYPR-NLM in an iterative formulation significantly reduces image noise and the image noise is comparable to or even lower than that generated using Iter-DECT. For the HYPR-NLM method, there are marginal edge effects in the difference image, suggesting the high-frequency details are well preserved. In addition, when the search window size increases from to , there are no significant changes or marginal edge effects in the HYPR-NLM difference images. The reference drawn from the comparison study includes: (1) HYPR-NLM significantly reduces the DECT material decomposition noise while preserving quantitative measurements and high-frequency edge information, and (2) HYPR-NLM is robust with respect to parameter selection.